Tailored XZZX codes for biased noise
Tailored XZZX codes for biased noise
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DOI：
10.1103/physrevresearch.5.013035
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发表时间：
2022-03
影响因子：
4.2
通讯作者：
Qiang-Da Xu;Nam Mannucci;Alireza Seif;Aleksander Kubica;S. Flammia;Liang Jiang
中科院分区：
文献类型：
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作者：
Qiang-Da Xu;Nam Mannucci;Alireza Seif;Aleksander Kubica;S. Flammia;Liang Jiang
由于苛刻的阈值和资源要求，通用错误的量子纠错（QEC）具有挑战性。有趣的是，当物理噪声有偏差时，我们可以根据噪声调整QEC方案以提高性能。在这里，我们研究了一族具有XZZX型稳定子生成元的码，包括一组从五量子比特码推广而来的循环码和一组我们称之为广义复曲面码（GTC）的拓扑码。我们表明，这些XZZX代码是非常有效的量子比特，如果适合偏置噪声。为了表征代码的性能，我们使用的概念，有效距离，它概括了代码距离的情况下，有偏噪声和构成代理的逻辑故障率。我们发现，XZZX码可以实现一个有利的资源缩放在有偏噪声下的度量。我们还表明，XZZX码具有显着高的阈值，达到什么是可实现的随机码，而且它们可以有效地使用匹配解码器解码。最后，通过只增加一个标志量子比特，XZZX码可以实现容错QEC，同时保持其大的有效距离。结合，我们的研究结果表明，定制的XZZX码提供了一个资源有效的计划，容错QEC对偏置噪声。
Quantum error correction (QEC) for generic errors is challenging due to the demanding threshold and resource requirements. Interestingly, when physical noise is biased, we can tailor our QEC schemes to the noise to improve performance. Here we study a family of codes having XZZX-type stabilizer generators, including a set of cyclic codes generalized from the five-qubit code and a set of topological codes that we call generalized toric codes (GTCs). We show that these XZZX codes are highly qubit efficient if tailored to biased noise. To characterize the code performance, we use the notion of effective distance, which generalizes code distance to the case of biased noise and constitutes a proxy for the logical failure rate. We find that the XZZX codes can achieve a favorable resource scaling by this metric under biased noise. We also show that the XZZX codes have remarkably high thresholds that reach what is achievable by random codes, and furthermore they can be efficiently decoded using matching decoders. Finally, by adding only one flag qubit, the XZZX codes can realize fault-tolerant QEC while preserving their large effective distance. In combination, our results show that tailored XZZX codes give a resource-efficient scheme for fault-tolerant QEC against biased noise.